Related papers: Bilinear optimal control for weak solutions of the…
In this paper we study a bilinear optimal control problem associated to a chemo-repulsion model with linear production term. We analyze the existence, uniqueness and regularity of pointwise strong solutions in a bidimensional domain. We…
In this paper, we study an optimal control problem for a coupled non-linear system of reaction-diffusion equations with degenerate diffusion, consisting of two partial differential equations representing the density of cells and the…
We consider a bilinear optimal control problem associated to the following chemotaxis-consumption model in a bounded domain $\Omega \subset \mathbb{R}^3$ during a time interval $(0,T)$: $$\partial_t u - \Delta u = - \nabla \cdot (u \nabla…
In the present work we investigate an optimal control problem related to the following chemotaxis-consumption model in a bounded domain $\Omega\subset \mathbb{R}^3$: $$\partial_t u - \Delta u = - \nabla \cdot (u \nabla v), \quad \partial_t…
In this paper, we consider an optimal bilinear control problem for the nonlinear Schr\"{o}dinger equations with singular potentials. We show well-posedness of the problem and existence of an optimal control. In addition, the first order…
In this work we introduce a new optimal control algorithm for the Keller-Segel chemo-attraction system, where both boundary and distributed controls are considered and both are associated with introducing/removing the amount of chemical…
In this paper we study the following three-dimensional parabolic-parabolic chemo-repulsion model with potential production, logistic reaction and bilinear control, defined in $Q=(0,T)\times\Omega$: \begin{equation*}\label{eq0} \left\{…
In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former.…
In this paper, we address a distributed control problem for a system of partial differential equations describing the evolution of a tumor that takes the biological mechanism of chemotaxis into account. The system describing the evolution…
We study the solutions of the two-dimensional Keller-Segel system describing chemotaxis. The Keller-Segel system as well as the properties of the blow-up set has been extensively studied. In this paper we obtain generalized solutions for…
In this paper we study a bilinear optimal control problem associated to a 3D chemo-repulsion model with linear production. We prove the existence of weak solutions and we establish a regularity criterion to get global in time strong…
The mathematical modeling of numerous real-world applications results in hierarchical optimization problems with two decision makers where at least one of them has to solve an optimal control problem of ordinary or partial differential…
In this paper, we study chemotaxis effect vs logistic dampening on boundedness for the two-dimensional minimal Keller-Segel model with logistic source in a 2-D smooth and bounded domain. It is well-known that this model allows only for…
We consider constrained bilinear optimal control of second-order linear evolution partial differential equations (PDEs) with a reaction term on the half line, where control arises as a time-dependent reaction coefficient and constraints are…
We consider a bilinear optimal control for an evolution equation involving the fractional Laplace operator of order $0<s<1$. We first give some existence and uniqueness results for the considered evolution equation. Next, we establish some…
This paper concerns a distributed optimal control problem for a tumor growth model of Cahn-Hilliard type including chemotaxis with possibly singular potentials, where the control and state variables are nonlinearly coupled. First, we…
It is known that in two dimensions the classical Keller-Segel model can lead to cell aggregation. This behavior can be controlled by adding a logistic growth term with quadratic decay. Researchers have tried to find weaker damping…
This paper investigates an optimal control problem associated with a two-dimensional multi-species Cahn-Hilliard-Keller-Segel tumor growth model, which incorporates complex biological processes such as species diffusion, chemotaxis,…
We propose and analyze an optimal control problem associated with a Keller-Segel type parabolic system with chemoattraction, modeling the glioblastoma growth in a bi-dimensional bounded domain, influenced by the presence of oxygen where the…
The Keller-Segel model is a system of partial differential equations that describes the movement of cells or organisms in response to chemical signals, a phenomenon known as chemotaxis. In this study, we analyze a doubly parabolic…